A furniture store purchased a dining room table and marked it up 150% from the original cost of $456. A week later, the store placed the dining room table on sale for 30% off. What was
the discount price?

Step-by-step explanation:

Identify what you are asked to find.What is the sales tax?

Choose a variable to represent it.Let t = sales tax.

Write a sentence that gives the information to find it.The sales tax is 6.5% of the purchase price.

Translate into an equation. (Remember to change the percent to a decimal).

Simplify.t = 25.48

Check: Is this answer reasonable?Yes, because the sales tax amount is less than 10% of the purchase price.

Write a complete sentence that answers the question.The sales tax is $25.48.

(b)

Identify what you are asked to find.What is the total cost of the bicycle?

Choose a variable to represent it.Let c = total cost of bicycle.

Write a sentence that gives the information to find it.The total cost is the purchase price plus the sales tax.

Translate into an equation. (Remember to change the percent to a decimal).

Simplify.c = 417.48

Check: Is this answer reasonable?Yes, because the total cost is a little more than the purchase price.

Write a complete sentence that answers the question.The total cost of the bicycle is $417.48.

Exercise  6.3.1 :

Find (a) the sales tax and (b) the total cost: Alexandra bought a television set for $724 in Boston, where the sales tax rate was 6.25% of the purchase price.

Answer a

Answer b

Exercise  6.3.2 :

Find (a) the sales tax and (b) the total cost: Kim bought a winter coat for $250 in St. Louis, where the sales tax rate was 8.2% of the purchase price.

Answer a

Answer b

Example  6.3.2 :

Evelyn bought a new smartphone for $499 plus tax. She was surprised when she got the receipt and saw that the tax was $42.42. What was the sales tax rate for this purchase?

Solution

Identify what you are asked to find.What is the sales tax rate?

Choose a variable to represent it.Let r = sales tax.

Write a sentence that gives the information to find it.What percent of the price is the sales tax?

Translate into an equation.

Divide.

499r499=42.42499(6.3.1)

Simplifyr = 0.085

Check. Is this answer reasonable?Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.

Write a complete sentence that answers the question.The sales tax rate is 8.5%.

Exercise  6.3.3 :

Diego bought a new car for $26,525. He was surprised that the dealer then added $2,387.25. What was the sales tax rate for this purchase?

Answer

Exercise  6.3.4 :

What is the sales tax rate if a $7,594 purchase will have $569.55 of sales tax added to it?

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)